Prove that u(x) is in $L^{\infty}\left(B(0,1)\right)$

Question

Let $B(0,1)\subset \mathbb{R}^{N}$, $N>1$. And the function $$u(x):=\ln\left(\ln\left(1+\frac{1}{|x|}\right)\right),\quad x\in B(0,1)\backslash \{0\}$$

How can I prove that $u\notin L^{\infty}\left(B(0,1)\right)$?